Chapter 11: The Chi-Square Distribution
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58 Terms
1
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Degrees of freedom
which depends on how chi-square is being used.
2
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The population standard deviation is 𝜎\=√2(df).
3
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Population mean
μ \= df
4
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Random variable
X^2
5
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Squared standard normal variables
χ2 \= (Z1)^2 + (Z2)^2 + ... + (Zk)^2
6
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The null and alternative hypotheses for GOF
may be written in sentences or may be stated as equations or inequalities.
7
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Null hypothesis
The observed values of the data values and expected values are values you would expect to get.
8
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Degrees of freedom GOF
Number of categories - 1
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The goodness of fit is usually right-tailed
10
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Large test statistic
Observed values and corresponding expected values are not close to each other.
11
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Expected value rule
Needs to be above 5 to be able to use the test
12
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Test of independence
Determines whether two factors are independent or not
13
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The null hypothesis for independence
states that the factors are independent
14
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The alternative hypothesis for independence
states that they are not independent (dependent).
15
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Independence degrees of freedom
(number of columns -1)(number of rows - 1)
16
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Expected value formula
(row total)(column total) / total number surveyed
17
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Test for Homogeneity
used to draw a conclusion about whether two populations have the same distribution
18
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Ho for Homogeneity
The distributions of the two populations are the same.
19
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Ha for Homogeneity
The distributions of the two populations are not the same.
20
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The test statistic for Homogeneity
Use a χ2 test statistic. It is computed in the same way as the test for independence.
21
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Goodness-of-Fit
decides whether a population with an unknown distribution "fits" a known distribution.
22
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Ho for GOF
The population fits the given distribution
23
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Ha for GOF
The population does not fit the given distribution.
24
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Independence
decides whether two variables are independent or dependent. There will be two qualitative variables and a contingency table will be constructed.
25
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Ho for Independence
The two variables (factors) are independent.
26
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Ha for Independence
The two variables (factors) are dependent.
27
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Homogeneity
decides if two populations with unknown distributions have the same distribution as each other. There will be a single qualitative survey variable given to two different populations.
28
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Ho of Homogeneity
The two populations follow the same distribution.
29
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Ha of Homogeneity
The two populations have different distributions.
30
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Degrees of freedom
which depends on how chi-square is being used.
31
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The population standard deviation is 𝜎\=√2(df).
32
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Population mean
μ \= df
33
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Random variable
X^2
34
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Squared standard normal variables
χ2 \= (Z1)^2 + (Z2)^2 + ... + (Zk)^2
35
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The null and alternative hypotheses for GOF
may be written in sentences or may be stated as equations or inequalities.
36
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Null hypothesis
The observed values of the data values and expected values are values you would expect to get.
37
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Degrees of freedom GOF
Number of categories - 1
38
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The goodness of fit is usually right-tailed
39
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Large test statistic
Observed values and corresponding expected values are not close to each other.
40
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Expected value rule
Needs to be above 5 to be able to use the test
41
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Test of independence
Determines whether two factors are independent or not
42
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The null hypothesis for independence
states that the factors are independent
43
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The alternative hypothesis for independence
states that they are not independent (dependent).
44
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Independence degrees of freedom
(number of columns -1)(number of rows - 1)
45
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Expected value formula
(row total)(column total) / total number surveyed
46
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Test for Homogeneity
used to draw a conclusion about whether two populations have the same distribution
47
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Ho for Homogeneity
The distributions of the two populations are the same.
48
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Ha for Homogeneity
The distributions of the two populations are not the same.
49
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The test statistic for Homogeneity
Use a χ2 test statistic. It is computed in the same way as the test for independence.
50
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Goodness-of-Fit
decides whether a population with an unknown distribution "fits" a known distribution.
51
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Ho for GOF
The population fits the given distribution
52
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Ha for GOF
The population does not fit the given distribution.
53
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Independence
decides whether two variables are independent or dependent. There will be two qualitative variables and a contingency table will be constructed.
54
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Ho for Independence
The two variables (factors) are independent.
55
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Ha for Independence
The two variables (factors) are dependent.
56
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Homogeneity
decides if two populations with unknown distributions have the same distribution as each other. There will be a single qualitative survey variable given to two different populations.
57
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Ho of Homogeneity
The two populations follow the same distribution.
58
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Ha of Homogeneity
The two populations have different distributions.